Entropy aided K-t Group Sparse SENSE method for highly accelerated dynamic MRI

INTRODUCTION: Over the last few years, the combination of Compressed sensing (CS) and parallel imaging have been of great interest to accelerate MRI. For dynamic MRI, K-t sparse SENSE (K-t SS) has been proposed [1] for combining the CS based K-t Sparse method [2] with SENSE. Recently, K-t group sparse method (K-t GS) [3] has been shown to outperform K-t Sparse for single coil reconstruction, by exploiting the sparsity and the structure within the sparse representation (x-f space) of dynamic MRI. In this work, we propose to extend K-t GS to parallel imaging acquisition in order to achieve higher acceleration factors by exploiting the spatial sensitive encoding from multiple coils. This approach has been called K-t group Sparse SENSE (K-t GSS). In contrast with the previous single-coil based K-t GS method for which a performance parameter is manually optimized for every frequency encode; we propose an entropy based scheme for automatic selection of this parameter. Results from retrospectively undersampled cardiac gated data show that K-t GSS outperformed K-t sparse SENSE at high acceleration factors (up to 16 fold). THEORY: Let X be the signal in x-f space whose elements Xi {i=1, 2,.., N} are assigned to K distinct groups {g1,g2,..,gK} which are non overlapping and whose union gives the signal X. K-t GS formulation is given as: minX||X||1,2 subject to ||AX b||2 ≤ σ (1), where ||X||1,2 is the mixed l1-l2 norm given as ||X||1,2 =||X1||2+||X2||2+.......+||XK||2, ||Xj||2 being the l2 norm of the vector containing all elements in x-f space assigned to the group {gj} , A is the encoding matrix comprising the inverse Fourier transform along temporal dimension, Fourier transform along spatial dimension and the undersampling operator, b is the set of measure-